Problem: Luis is 2 times as old as Daniel. 35 years ago, Luis was 7 times as old as Daniel. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Luis and Daniel. Let Luis's current age be $l$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $l = 2d$ 35 years ago, Luis was $l - 35$ years old, and Daniel was $d - 35$ years old. The information in the second sentence can be expressed in the following equation: $l - 35 = 7(d - 35)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = l / 2$ . Substituting this into our second equation, we get: $l - 35 = 7($ $(l / 2)$ $- 35)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $l - 35 = \dfrac{7}{2} l - 245$ Solving for $l$ , we get: $\dfrac{5}{2} l = 210$ $l = \dfrac{2}{5} \cdot 210 = 84$.